In order to get a better understanding of how this system could perform in real world scenarios we set out to explore how changing the initial population could influence the systems performance. The first parameter explored was the size of the population. This is important to understand as in a real world smart-city it may be practical to divide the population into multiple smaller community energy systems. While indirect reciprocity facilitated by reputation, which we model as social capital, has been found to be beneficial to the performance of populations in public goods games, this has rarely been the case with larger populations [1]}. The network topology used has a major impact on the viability of social behaviour, and heavily clustered smaller societies have been found to promote more cooperation than larger networks [2]}, [3]}. For our mechanism it is therefore important to determine which population sizes facilitate social behavior and thus maximise the average agent satisfaction. To compare with the 96 population simulation runs already discussed, we re-ran the simulation with a variety of population sizes between 24 and 192 agents. These numbers were chosen in order to be between \(25\%\)  and \(200\%\)  of the initial population of 96 agents. In order to minimise the variables in the system the availability of energy in the system was linearly scaled to meet the demand required. Table REF  shows how the systems behaviour changed by adjusting only the population size. The smallest population of 24 agents adopted the social strategy far more frequently than the larger populations, with the social strategy taking control on 84 of the 100 simulation runs. This is a clear contrast with the largest population of 192 agents, which adopted the social strategy only once in all 100 simulation runs. However, while the smallest population adopted the social strategy more often, the average satisfaction at the end of the simulation was only \(0.623\) , which is similar to the average satisfaction seen with the largest populations selfish runs which averaged \(0.632\) .
